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Mathematics and statistics course of the University of Oxford

Year 2 of the mathematics and statistics course of the University of Oxford

Probability, statistics and options II course of the University of Oxford

Past exam of the Probability, statistics and options II course of the University of Oxford

2011

The <monotone convergence theorem> states that for measurable functions $0\leq f_1\leq f_2\leq\cdots$ converging pointwise to $f$, the limit is measurable and
$$
\boxed{\int f\,d\mu=\lim_{n\to\infty}\int f_n\,d\mu.}
$$
Both sides may be infinite. Monotonicity and nonnegativity replace any need for an integrable dominating function.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / D / D4 / a / Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / D / D4 / a / Solution

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Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / D / D4 / a / Solution

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